Question

if y = 2 log sqft( 1 - cos x/ 1 + cos x) show that DY/DX equals to cosec x

Answer 1

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Answer 2

y= log(1-cos x/1+cos x)

y=log(1-cos x)-log(1+cos x)……..[by properties of logarithm  log(a/b)=log a-logb]

Differentiating both sides we get,

dy/dx=[{1/(1-cos x)}.sin x]-[{1/(1+cos x)}.(-sin x)]

=> {sin x/(1-cos x)} + {sin x/(1+cos x)}

=> (sin x+sinx)/sin^2 x……..solving (1-cosx) and (1+cos x) in denominator we get sin^2 x.

=> 2sin x/ sin^2 x

=>2/ sin x

Reciprocal of sinx is cosec x.

=>2 cosec x  (Hence proved)